$a)_{}$ $2x^2+4xy+2y^2_{}$
$=2.(x^2+2xy+y^2)_{}$
$=2.(x+y)^2_{}$
$b)_{}$ $x^2+y^2-2xy-4x-4y_{}$
$=(x^2-2xy+y^2)-(4x-4y)_{}$
$=(x-y)^2-4.(x-y)_{}$
$=(x-y)(x-y-4)_{}$
$c)_{}$ $x^4-4x^3-8x^2+8x_{}$
$=x.(x^3-4x^2-8x+8)_{}$
$=x.[ (x+2)(x^2-2x+4-4x.(x+2)] _{}$
$=x.(x+2)(x^2-2x+4-4x)_{}$
$=x.(x+2)(x^2-6x+4)_{}$
$d)_{}$ $x^3+2x^2-3_{}$
$=x^3-x^2+3x^2-3x+3x-3_{}$
$=x^2.(x-1)+3x.(x-1)+3.(x-1)_{}$
$=(x-1)(x^2+3x+3)_{}$
$e)_{}$ $x^2+5x-6_{}$
$=x^2+6x-x-6_{}$
$=x.(x+6)-(x+6)_{}$
$=(x+6)(x-1)_{}$
